Sam will sit on the floor of the tank sometimes, that spot in the tank being the nearest spot to me while I'm sitting here at my desk (at the front, in the corner nearest me). It has a real 'dog at your feet' feeling, but at the same time, I want to make sure fish actually do this and he's not sick.

Water is only 3-4 days old and was treated properly, is at temp, and he's eating now too(!), and swims quite happily when he's not 'chilling'. I've read other posts from ppl saying their fish rest on rocks, plants, are actually 'lazy', and in some cases fat, which goes against my impression of how fish behave in the wild.

One more thing, when they sleep, is it normal for them to actually kind of curl up somewhere and sleep while physically resting? I was under the impression they constantly swam/floated while swimming.

Also, should the water have any particular smell?
Mine smells a little bit chemically, but not chlorine. Maybe this is the treatment pellet at work? The smell of the plastic lid? The water is clear and not ruddy or gunky. Does the ammonia build up that fast so as to produce a smell?

Yeah bettas are relatively lazy. Partially due to the enormous fins they have to lug around, partially due to the stagnant water of their natural habitat. You will notice that the faster the current in the natural habitat is, the more active the fish is. Danios, for instance, are found in fast-flowing streams and are therefore extremely active. Bumblebee gobies, found in slow-moving estuaries, are quite idle.

Ideally your water should be pretty much odorless. It is not uncommon for you to detect the smell of plastic or water additives if you actually sniff, but it shouldn't be overwhelming. If a fish or invert has died in your tank you may notice a suspiciously rotten smell, even from across the room. Likewise if you have a bloom of anaerobic bacteria (which is only really a risk in large tanks with deep sand or gravel beds where air cannot circulate through the substrate) you will also be able to smell a rotten-egg smell (produced by the hydrogen-sulphide gas that the anaerobic bacteria give off).

Ammonia pruduces no smell that I am aware of, but a good visual indicator of ammonia buildup is that ammonia will turn the water whitish and cloudy.

nope- fish generally stop swimming when they sleep- except for sharks that have to keep moving to breath. A lot of betta will curl up on ir in their plants- I once found mine sleeping face down in the middle of the stalks like she dove in there- others sleep in their caves, or find the warmest or coolest spot, or the place where the current is gentlest.

Thanks guys for the input. Hearing these things kinda put my mind to rest, I'm not alone, other people's fish are lazy too hehe.
Yeah last night mine was kinda lazing around, I think he just wanted to go to bed and was waiting for me to turn out the lights. I will buy him a terracotta cave or a piece of driftwood this weekend. He likes to hide behind the heater wire but that's not really shielding him from light, he may want a nice dark place to nap.

Today he ate breakfast and he's swimming around happily. He still comes to keep me company sometimes in the corner closest to my desk, which is pretty neat.

The water has a plasticky smell if I was gonna name it, I suspect its a combination of the lid and the water treatment. It doesn't have any rotten or astringent smells like rot or ammonia or pungent urine or anything. Water is clear too.

My betta hangs out or "chills" at the top of the water, with the top of his head touching the surface, and just floats for a while in different spots. Sometimes he rests ontop of his Taj Mahal palace. Is this the same thing?

And then my real question.. At times, especially in the middle of the night or early morning; he swims really, really fast around the tank and freaking JUMPS out of the water several times. I have a lid on my tank, thank god.. I'm sure I or my cat would have found him dead on the floor. So this is kinda freaking me out. I'm very entertained by it, but he's never done that before. I bought him last summer. I did leave town for a month and my aunt did not take very good care of him... or my cats.. or my orchids for that matter. So I thought since I moved and brought him home and cleaned his tank (It was awful!!!) he was just super excited and happy.